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Almost every set in exponential time is P-bi-immune

  • Elvira Mayordomo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 629)

Abstract

A set A is P-bi-immune if neither A nor its complement has an infinite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). Using resource-bounded measure, we prove that the class of P-bi-immune sets has measure 1 in E. This implies that “almost” every language in E is P-bi-immune. A bit further, we show that every p-random (pseudorandom) language is E-bi-immune. Regarding the existence of P-bi-immune sets in NP, we show that if NP does not have measure 0 in E, then NP contains a P-bi-immune set. Another consequence is that the class of ≤ 1-tt P -complete languages for E has measure 0 in E. In contrast, using the approach of resource-bounded category, it is shown that in E, the class of P-bi-immune languages lacks the property of Baire (the Baire category analogue of Lebesgue measurability).

Keywords

Complexity Class SIAM Journal Random Oracle Exponential Time Meaningful Measure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • Elvira Mayordomo
    • 1
  1. 1.Departament de Llenguatges i Sistemes InformaticsUniv. Politècnica de CatalunyaBarcelonaSpain

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